1. DIPARTIMENTO DI FISICA Luca Sorriso-Valvo Sezione di Cosenza Intermittency in solar wind induced electric field Roberto Bruno Vincenzo Carbone

2. INTRODUCTION We analyse PDFs of the solar wind induced electric field e=-vxb We show that the induced electric field is characterized by intermittency. Breech et al. (JGR, 2003) reported on PDFs of the interplanetary induced electric field, using the NSSDC Omnitape database, including 30 years of hourly averaged spacecraft measurements of solar wind fields PDFs of the induced electric field from their data show exponential tails

3. Data used by Breech et al. include: 1hour averages different solar activity levels fast and slow solar wind (and interfaces between them). Exponential tails for field components has been previously investigated theoretically and using numerical data. If velocity and magnetic field components have gaussian PDFs, and satisfy some hypothesis about their correlations -e z =v x b y -v y b x, P(v i )=P(b i )= gaussian + {hp. on corr.} P(e z ) = exponential tails Milano et al., PRE 65, 026310, 2002 BACKGROUND

4. SIMULATIONS The current j data: 2×10 7 pts simulations: H. Politano & A. Pouquet, z     v ± B/(4  ) 1/2 are the Elsasser variables,       , F  external forcing, P * total pressure DNS of the 2-dimensional MagnetoHydroDynamics equations R e ~ 1600 Pseudo-spectral method, resolution 1024² induced electric field PDF exponential tails

5. SOLAR WIND DATA Fast windSlow wind data: ~ 10 4 pts, sampling time:  sec velocity and magnetic field  e=-vxb Separation in fast and slow streams Helios 2 spacecraft: in situ measurements We thus define: fast streams with v 0 > 550 km/sec slow streams with v 0 < 450 km/sec

6. PDFs of the field components We compute the PDFs of the components and the magnitudes of the fields ( v, b and e ) in the SE frame ( x || V 0 ) using the standardized variables:

7. xmagnitudezy magnetic field velocity = x induced electric field the only case presenting exponential tails... almost gaussian PDFs! fast wind slow wind (not true in the x || B 0 frame)

8. Our results are quite different from those by Breech et al. Possible reasons for measured PDFs differences: the different time resolution the mixing of fast and slow wind, as well as the non- steady interstream regions, in OMNITAPE data the widely diffrent solar activity in OMNITAPE data The mixing of different physical conditions could be responsible for the exponential tails found by Breech et al. Possible reasons for differences with respect to theoretical and numerical results: violation of conditions about correlations, anisotropy… Comments...

9. INTERMITTENCY Look at the Flatness of the field increments at different scales . The gaussian reference value is F=3. F>3 indicates rising tails of the PDFs. The growth of F toward the small scales is the signature of intermittency. We study the intermittency of the induced electric field. Flatness fast windslow wind

10. xyxy Small scale: stretched exponential Inertial range: raising tails Large scale: nearly Gaussian INTERMITTENCY by PDFs fast windslow wind

11. A multifractal model for PDFs According to multifractal models, the P(  f) at scale  is obtained as superposition of Gaussians, each one: ...describing the statistics in different regions of space ...with different variance  ...opportunely weighted : We must choose a model for the weight of each gaussian in the convolution. For example: Log-normal distribution of the variances  Castaing et al., Phys. D 46, 177 (1990) As ² increases, L(  ) is wider  more and more Gaussians of different width are summed  the tails of P(  f) become higher  ²= 0, L(  ) is a  - function centered in  0  computing the convolution, the resulting P(  f) at scale  is Gaussian

12. The parameter ² is found to behave as a power-law of the scale and its scaling properties can be used to characterize the shape of the PDFs   ² max, the maximum value of the parameter ² within its scaling range, representing the non-gaussianity of the PDF  , the ‘slope’ of the power-law, representing the efficiency of the non-linear cascade Relevant parameters of the model

13. Results for e components 0.09±0.010.86±0.03slow 0.06±0.020.74±0.04fast  ² max wind 0.20±0.040.37±0.03v slow 0.44±0.050.51±0.04v fast  ² max field Results for v and b 0.18±0.030.73±0.04b slow 0.19±0.020.88±0.04b fast y x  ² max wind 0.12±0.020.79±0.03slow 0.29±0.030.67±0.04fast Results for the induced electric field

14. CONCLUSIONS From the analysis of the Helios 2 solar wind time series, we find that the induced electric field components have quasi-Gaussian probability distribution function for both fast and slow wind. The model presented by Milano et al. is not reliable to reproduce the solar wind induced electric field features as observed from Helios 2 data. This could be due to the presence of correlations between the field components, which are more complex than cross-helicity type. The induced electric field is shown to be intermittent through the analysis and modeling of the field increments PDFs. Intermittency could in fact be a candidate responsible for long- range correlations characterizing the solar wind fields.